An Optimal Algorithm for Closest-Pair Maintenance

Abstract

Given a set S of n points in k-dimensional space, and an L t metric, the dynamic closest pair problem is deened as follows: nd a closest pair of S after each update of S (the insertion or the deletion of a point). For xed dimension k and xed metric L t , we give a data structure of size O(n) that maintains a closest pair of S in O(log n) time per insertion… (More)